Protective relaying generally involves the performance of one or more of the following functions in connection with a protected power or energy system: (a) monitoring the system to ascertain whether it is in a normal or abnormal state; (b) metering, which involves measuring certain electrical quantities; (c) protection, which typically involves tripping a circuit breaker in response to the detection of a short-circuit condition; and (d) alarming, which provides a warning of some impending problem. Fault location is associated with the protection function. It involves measuring critical system parameters and, when a fault occurs, quickly making an estimate of the fault location so that the faulted line can be returned to service as quickly as possible.
The major types and causes of faults are: (1) insulation faults, caused by design defects, manufacturing defects, improper installation, and aging insulation; (2) electrical faults, caused by lightning surges, switching surges, and dynamic overvoltages; (3) mechanical faults, caused by wind, snow, ice, and contamination; and (4) thermal faults, caused by overcurrent and overvoltage conditions.
A fault may cause current in one or more of the phase lines (referred to herein as the "a", "b", and "c" phases) to be diverted to ground, to a neutral line (denoted "n"), or to another phase line. The phasor diagrams in FIGS. 1A-1E illustrate the effect of faults on the system voltages and currents. The diagrams are for effectively grounded systems wherein the neutral is solidly grounded. In addition, the diagrams are for the ideal case of a zero fault resistance (R.sub.F =0). (Many of the prior art fault location systems work well with such an ideal case. The present invention is directed to cases involving non-zero fault resistance.) However, they are illustrative of the effects of faults on other types of systems, e.g., ungrounded and impedance grounded systems. In the diagrams, the dotted, uncollapsed voltage triangle exists in the source (the generator) and the maximum collapse is at the fault location. The voltages between the source and fault will vary between these extremes. The diagrams depict the effects of various types of faults on the currents and voltages (represented by phasors) in the system. FIG. 1A depicts the phasors for normal, balanced conditions; FIG. 1B depicts the phasors for a three-phase fault (V.sub.ab =V.sub.bc =V.sub.ca =0 at the fault); FIG. 1C depicts the phasors for a phase b-to-phase c fault (V.sub.bc =0 at the fault); FIG. 1D depicts the phasors for a phase b-to-phase c-to-ground fault (V.sub.bc =V.sub.bg =V.sub.cg =0 at the fault); and FIG. 1E depicts the phasors for a phase a-to-ground fault (V.sub.ag =0 at the fault).
The present invention relates to fault location in connection with electrical conductors of a power transmission system. One function of protective relaying systems is to estimate the location and resistance of the fault. For example, as described in U.S. Pat. No. 4,906,937, Mar. 6, 1990, titled "Method and a Device for Fault Location in the Event of a Fault on a Power Transmission Line" (assigned to Asea Brown Boveri AB, Vasteras, Sweden), it is normally desirable to estimate the distance from a measuring station to a possible fault and to determine the magnitude of the fault resistance.
The basic principles of fault location are well known. Typically, measured values are obtained with the aid of measuring transformers in a relay located adjacent to a protected line. Present-day techniques employ analog-to-digital (A/D) conversion and filtering of the measured values. The filtered digital values are then processed by various equations to determine the fault distance and the magnitude of the fault resistance.
There are several known distance protection equations. Two of the most ordinary ones will be briefly described with reference to FIG. 2A, which depicts a line between stations P and Q on which a fault to ground has arisen at point F. Both of these equations assume knowledge of the faultless line impedance Z.sub.PQ on the protected line segment between two measuring stations P and Q. After the detection of a fault, the voltages U.sub.P and U.sub.Q and the currents I.sub.P and I.sub.Q are measured in the respective stations. To eliminate the need for communication between the stations, the values measured at one of the stations are employed as a starting-point. If the assumption is made that a current I.sub.F flows through a fault resistance R.sub.F, producing a voltage U.sub.F across the fault resistance, the following relationship can be assumed: EQU U.sub.P =U.sub.PF +U.sub.F =.alpha.U.sub.PQ +U.sub.F =.alpha.Z.sub.PQ I.sub.P +R.sub.F I.sub.F ( 0.1)
where .alpha. is a parameter having a value in the range 0 to 1 and is an assumed measure of the fault position, and U.sub.PQ is an estimate of the voltage drop across the entire line. The U.sub.PQ estimate is determined with the aid of I.sub.P, which is measured.
Equation (0.1) is not directly solvable because it contains too many unknown parameters (i.e., U.sub.PF, U.sub.F, .alpha., R.sub.F, I.sub.F are unknown quantities). Therefore, certain assumptions must be made. It is common to assume that the fault current I.sub.F is proportional to the current measured in station P. That is, it is assumed that EQU I.sub.F =k.sub.1 I.sub.P ( 0.2)
This assumption is fulfilled if the voltages U.sub.P and U.sub.Q at P and Q have equal phases and if the phase angles for the impedances from the fault location F to the respective stations P, Q are equal. (This condition may be expressed: X.sub.S /R.sub.S =X.sub.R /R.sub.R =X.sub.L /R.sub.L, where X.sub.S and X.sub.R and X.sub.L respectively represent the source-end, remote-end, and line reactance, and R.sub.S, R.sub.R, and R.sub.L respectively represent the source-end, remote-end, and line resistance.) Equation (0.1) can then be written: EQU U.sub.P =.alpha.Z.sub.PQ I.sub.P +R.sub.F k.sub.1 I.sub.P =.alpha.Z.sub.PQ I.sub.P +R.sub.F1 I.sub.P ( 0.3)
where R.sub.F1 is an apparent fault resistance.
Another variant of the necessary assumption is to assume that the fault current is proportional to the current change at P when a fault has occurred. That is, it is assumed that EQU I.sub.F =k.sub.2 .DELTA.I.sub.P ( 0.4)
Therefore, equation (0.1) can be expressed: EQU U.sub.P =.alpha.Z.sub.PQ I.sub.P +R.sub.F k.sub.2 .DELTA.I.sub.P =.alpha.Z.sub.PQ I.sub.P +R.sub.F2 .DELTA.I.sub.P ( 0.5)
Equations (0.3) and (0.5) each comprise two unknown parameters, .alpha. and R.sub.F1 or R.sub.F2, respectively. This means that a linear regression (or some other problem solving technique) is required to solve for the unknown parameters.
When distance protection devices with fault location are used in connection with high voltage transmission lines, capacitive voltage transformers (CVTs) are usually used for the voltage measurement. It is well known that such voltage measurement devices cause measurement error voltages, called "CVT transients."
The above cited U.S. Pat. No. 4,906,937 describes a fault location system that specifically addresses the problem of CVT transients. The disclosed system is depicted schematically in FIG. 2B. As described in the patent, phase voltages U.sub.P and phase currents I.sub.P are measured on a high voltage network RST at a measuring station P. The patent discloses that either of the following two distance protection equations may be employed as a starting-point: EQU U.sub.PM1 =.alpha.Z.sub.PQ I.sub.P +R.sub.F1 I.sub.P +.DELTA.U.sub.CVT( 0.6) EQU U.sub.PM2 =.alpha.Z.sub.PQ I.sub.P +R.sub.F2 .DELTA.I.sub.P +.DELTA.U.sub.CVT ( 0.7)
If equation (0.6) is made the starting-point, the device for fault location is continuously switched and controls the state of the line. If equation (0.7) is made the starting-point, a least prescribed change of I.sub.P must be assumed to initiate the control of the state of the line. The measuring voltage U.sub.PM is obtained via a capacitive voltage divider 1 and a conventional transformer 2. The current I.sub.P is measured with a current transformer 3. The measured values are low-pass filtered in filters 4 and 5. The filtered voltage and current signals are converted to digital data by analog-to-digital conversion devices 6, 7. The instantaneous digitalized current and voltage values are supplied to a calculator 8, which processes the data to obtain estimated values of: .alpha., representing the fault position; R.sub.F1 and R.sub.F2, respectively representing the apparent fault resistance; and .DELTA.U.sub.CVT, representing the fault voltage. The values of .alpha., R.sub.F1, and R.sub.F2 are supplied to a logic unit 9 for comparison with upper and lower limit values .alpha..sub.min, .alpha..sub.max, RF.sub.min, and RF.sub.max, respectively. If the .alpha. and RF values lie within the stated limits, a decision B to trip is given.
A disadvantage of some prior art fault location systems is that non-linearities associated with the fault (e.g., a non-linear fault resistance R.sub.F) adversely influence the accuracy of the fault location estimation. Prior art systems that employ data obtained from opposite sides of the fault purportedly are capable of estimating the location of non-linear faults. For example, U.S. Pat. No. 5,072,403, Dec. 10, 1991, titled "Equipment for and Methods of Locating the Position of a Fault on a Power Transmission Line," discloses such a system. However, this and similar known systems assume that the data samples from the respective ends of the line are synchronized, i.e., sampled at the same time, and that the computed phase angles of the currents and voltages are relative to a common reference. A GPS (global positioning system) satellite has been employed to achieve such synchronization. Nonetheless, the requirement of such synchronization is a disadvantage in that it increases the cost and complexity and reduces the reliability of the system.
Another disadvantage of some prior art fault location systems is that they employ algorithms that are influenced by (1) the combined effects of the values of the fault resistance and load, (2) the outside network, (3) an unbalanced load, (4) a capacitance parallel to the fault, and (5) a line in parallel to the faulted line. The enumerated items adversely affect the accuracy and reliability of the fault location estimation provided by these systems. Moreover, some systems lose accuracy when used in association with long transmission lines (e.g., lines of about 150 miles or longer). This is because they employ a transmission line model (impedance or II) that does not recognize the distributed nature of the line impedance and admittance parameters (these distributed parameters are referred to hereinbelow as Z.sub.ld and Y.sub.ld).